Pretty cool stuff: the PlayStation 4 apparently runs on a version of FreeBSD 9.0 modified by Sony and renamed to 'Orbis OS'. Second generation developer kits use GNU GRUB to boot, and allow you to boot into a graphical or a console mode. Not much else is known at this point, but it's a fun bit of information, and perhaps a boon to homebrew developer and hackers.

Because there is a bunch of stuff that comes along with OpenGL that isn't necessary. Remember that OpenGL is designed as an abstraction layer to separate the graphics implementation from the hardware implementation, so the hardware can change and the software remain the same. An example are shaders, which are compiled on demand for the target graphics card. This is completely unnecessary on a console.

It is much better to design an API that is much more in line with how the hardware functions, and abstracts less of it away. It'll provide much more predictable and reliable results.

The PS3 had an implementation of OpenGL ES available. Nobody used it. Instead, they used Sony's API, which was closer to the hardware, and had much less overhead.

Even on the Xbox 360, the API used isn't really Direct3D 9. It's very similar, but again, it's closer to the hardware with less overhead than the desktop version.

While it's possible that Sony might provide an OpenGL implementation, they would only do so for the sake of portability. Most games would still use Sony's API instead, because portability isn't a big deal. Most game engines already abstract the rendering API away, so they can support D3D 9, D3D 11, OpenGL, OpenGL ES, and proprietary APIs on consoles. Very few games are written directly on top of one of those APIs anymore.